Aharonov-Bohm effect and geometric phases -- Exact and approximate topology
arXiv:1302.0456 · doi:10.1142/9789814472906_0016
Abstract
By analyzing an exactly solvable model in the second quantized formulation which allows a unified treatment of adiabatic and non-adiabatic geometric phases, it is shown that the topology of the adiabatic Berry's phase, which is characterized by the singularity associated with possible level crossing, is trivial in a precise sense. This topology of the geometric phase is quite different from the topology of the Aharonov-Bohm effect, where the topology is specified by the external local gauge field and it is exact for the slow as well as for the fast motion of the electron.
6 pages. Invited talk given at Tonomura FIRST International Symposium on Electron Microscopy and Gauge Fields, May 9-10, 2012, Tokyo, Japan